Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds

Abstract

Let $L$ be a nonnegative, self-adjoint operator on $L^2({\mathbb{R}}^n)$ with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space ${\mathcal{L}}_{-\Delta }^{2,\lambda }({\mathbb{R}}^n)$, in \cite{DXY} the quadratic Campanato space ${\mathcal{L}}_L^{2,\lambda }({\mathbb{R}}^n)$ is defined by a variant of the maximal function associated with the semigroup $\{e^{-tL}{\}}_{t\ge 0}$. On the basis of \cite{DX} and \cite{YY} this paper addresses the preduality of ${\mathcal{L}}_L^{2,\lambda }({\mathbb{R}}^n)$ through an induced atom (or molecular) decomposition. Even in the case $L=-\Delta$ the discovered predual result is new and natural.

19 pages

References in corpus (1)

• Gaussian heat kernel upper bounds via Phragmén-Lindelöf theorem